On the construction of optimal asymmetric quantum codes

Abstract

Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the constructed asymmetric quantum codes are optimal and different from the codes available in the literature.

Optimal Asymmetric Quantum Codes from the Euclidean Sums of Linear Codes

“…La Guardia [6,7] utilized classical Bose-Chaudhuri-Hocquenghem (BCH) codes to construct new classes of AQEC codes. Later, several classes of optimal AQEC codes have been constructed [8][9][10][11][12][13][14][15] . Chen et al [8] studied optimal AQEC codes by using negacyclic codes.…”

“…[11], Chen et al constructed some classes of optimal AQEC codes from constacyclic codes. Wang et al [13] also constructed six classes of new optimal AQEC codes from dual-containing constacyclic codes over finite fields by using the Cascading Style Sheets (CSS) construction. Recently, Xu et al [14] obtained two new classes of optimal asymmetric quantum codes from constacyclic codes.…”

Quantum stabilizer codes from Abelian and non-Abelian groups association schemes

“…Wang et al [21] studied the construction of nonadditive AQCs as well as constructions of asymptotically good AQCs derived from algebraic-geometry codes . Wang and Zhu [22] presented the construction of optimal AQCs. Ezerman et al [23] presented so-called CSS-like constructions based on pairs of nested subfield linear codes.…”